Noninvasive effective lung volume estimation

ABSTRACT

Methods for noninvasively measuring, or estimating, functional residual capacity or effective lung volume include obtaining carbon dioxide and flow measurements at or near the mouth of a subject. Such measurements are obtained during baseline breathing and during and shortly after inducement of a change in the subject&#39;s effective ventilation. The obtained measurements are evaluated to determine the amount of time required for exhaled carbon dioxide levels to return to normal—effectively an evaluation of carbon dioxide “washout” from the subject&#39;s lungs. Conversely, carbon dioxide and flow measurements may be evaluated to determine the amount of time it takes carbon dioxide to “wash in,” or reach peak levels within, the lungs of the subject following the change in the subject&#39;s effective ventilation. Apparatus for effective such methods are also disclosed.

CROSS-REFERENCE TO RELATED APPLICATION

This application is a continuation-in-part of application Ser. No. 10/121,219, filed on Apr. 11, 2002, pending.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates generally to techniques for determining functional residual capacity (FRC), the volume of gases that remain within a subject's lungs following exhalation, or, more broadly, the effective lung volume (ELV) of the subject, which includes gases that have diffused into the lung tissues. In particular, the present invention relates to techniques for noninvasively determining FRC or ELV.

2. Background of Related Art

Functional residual capacity (FRC) is the volume of gases, including carbon dioxide (CO₂), that remains within the lungs of a subject at the end of exhalation, or expiration. In healthy individuals, FRC usually comprises about 40% of total lung capacity, and typically amounts to about 1.8 liters to about 3.4 liters. FRC buffers against large breath-to-breath changes in the amount of carbon dioxide in the alveoli of the subject's lungs, which may be measured in terms of partial pressure of CO₂ (p_(ACO2)) or as a fraction of gases that comprise CO₂ (f_(ACO2)). With normal tidal volumes, p_(ACO2) and f_(ACO2) typically fluctuate by only about 2 mmHg or about 0.25%, respectively.

A number of authors contend that CO₂ is stored in the lungs in three different compartments: (1) the gas volume (V_(A) or FRC); (2) the lung tissue; and (3) the pulmonary blood present at any given time in the lung. The lung tissue and pulmonary blood compartments are often represented in terms of their equivalent gas volumes (i.e., scaled by their effective storage capacity) and denoted V_(tiS) and V_(blood). While FRC only accounts for the volume of gases (including CO₂) in the alveoli, effective lung volume (ELV) includes FRC, as well as gases that remain diffused within the tissues of the lungs of the subject at the end of exhalation and, therefore, accounts for gases in all three compartments.

While ELV is typically a slightly larger volume than FRC, these terms may be used interchangeably in the ensuing description for purposes of simplicity.

Each compartment equilibrates with changes in CO₂ at a different rate. Gedeon, A., et al., “Pulmonary blood flow (cardiac output) and the effective lung volume determined from a short breath hold using the differential Fick method,” J. CLIN. MONIT. 17:313-321 (2002) (hereinafter “Gedeon 2002”) teaches that V_(A) equilibrates instantly with changes in end tidal CO₂ (p_(ETCO2) when measured in terms of partial pressure and f_(etCO2) when measured in terms of the fraction of gases that comprise CO₂) and slowly (e.g., in about ten to about twenty seconds) with changes in p_(AC02) and content of CO₂ in arterial blood (c_(aCO2)), while it takes less time for V_(tis) and V_(blood) to equilibrate when p_(AC02) and c_(aCO2) change.

The relationship between a subject's chest wall and lungs and the elastic recoil of the lungs defines FRC and, thus, ELV. Lung diseases that change the elastic recoil of the lungs, including emphysema, asthma, and other restrictive diseases, affect FRC. Thus, FRC determinations may be useful in accurately diagnosing such conditions. FRC determinations are also useful in diagnosing and treating respiratory failure and hypoxemia.

In lungs with an FRC below the lung's closing capacity, the airways start to close before the end of a subject's exhalation, which results in a decrease of p_(AO2) and a mismatch between ventilation, or the movement of gases into and out of the lungs through the mouth, and perfusion, or the movement of gases across the gas/blood barrier between the alveoli of the lungs and the pulmonary capillaries that surround the alveoli. This is known in the art as V/Q mismatch or V_(T)/V_(Q) mismatch.

The currently available techniques for measuring FRC include full body plethysmography, nitrogen washout, and helium dilution. All of these methods require cumbersome equipment and, therefore, may not be suitable for use in an intensive care setting that is already crowded with equipment.

Gedeon 2002 proposed a noninvasive technique for determining ELV. Specifically, that technique includes measuring the {dot over (V)}_(M)CO₂ and f_(etCO2) of a subject, having the subject hold his or her breath for three seconds, the re-measuring {dot over (V)}_(M)CO₂ and f_(etCO2). For the first breath following the breath-hold, f_(etCO2) increases and {dot over (V)}_(M)CO₂, which is calculated over the duration of the breath hold and the subsequent breath, decreases. Assuming, due to buffering by the CO₂ stores of the ELV, that {dot over (V)}_(B)CO₂ (i.e., CO₂ passing from the pulmonary capillary blood into the alveoli of the lung) does not change during breath-holding, Gedeon contends that the decrease in {dot over (V)}_(M)CO₂ must have resulted from the CO₂ going into the lung stores of CO₂: [f _(etCO2 POST) −f _(etCO2 PRE) ]×{circumflex over (V)} _(A) ^(*) =[{dot over (V)} _(M) CO _(2PRE) −{dot over (V)} _(M)CO_(2POST) ]×[T _(breath) +T _(breathhold)] where [{dot over (V)}_(M)CO_(2PRE) and {dot over (V)}_(M)CO_(2POST) refer to measurements obtained respectively before and after the breath-holding maneuver.

In addition to this relationship, Gedeon developed equations that relate pulmonary capillary blood flow (PCBF or, for the sake of simplicity in the ensuing equations, {dot over (Q)}) of the subject to the subject's ELV. Two of these equations compare the pre-breathhold conditions to the post-breathhold conditions and the pre-breathhold conditions to the recovery conditions. The ELV of an ELV and PCBF data pair that satisfies both of these equations is considered to be the subject's actual ELV.

The technique of Gedeon 2002 is believed to provide inaccurate data, as it is based on the assumption that “CO₂ inflow [may] not [be] significantly affected” by breath-holding, while breath-holding will cause a change in p_(ACO2). This assumption is inconsistent with the Fick equation, in which {dot over (V)}_(B)CO₂ changes linearly with p_(ACO2) while PCBF and the amount of CO₂ in the venous blood (c_(vCO2) or, as Gedeon2002 refers to it, Pven) remain constant.

In view of the foregoing, it is apparent that there is a need for a technique for accurately, noninvasively measuring FRC or ELV in virtually any healthcare setting.

SUMMARY OF THE INVENTION

The present invention includes methods for noninvasively measuring, or estimating, FRC or ELV, as well as apparatus and systems for obtaining FRC and ELV measurements with minimal invasiveness.

As an example of a method for noninvasively measuring, or estimating, FRC or ELV in accordance with teachings of the present invention, carbon dioxide and flow measurements may be obtained at or near the mouth of a subject. Such measurements are obtained during baseline, or “normal,” breathing, as well as during and shortly after inducement of a change in the subject's effective ventilation. For example, measurements may be obtained during or shortly following a rebreathing maneuver, in which a subject inhales gases including an above-normal amount of CO₂. Continuing with the rebreathing example, the obtained measurements are evaluated to determine the amount of time required for exhaled CO₂ levels to return to normal-effectively an evaluation of CO₂ “washout” from the subject's lungs. Conversely, CO₂ and flow measurements may be evaluated to determine the amount of time it takes CO₂ to “wash in,” or reach peak levels within, the lungs of the subject following rebreathing. Of course, when other techniques are used to generate a perturbation, or change, in the effective ventilation (i.e., the total ventilation less the wasted ventilation due to deadspace associated with the apparatus, the individual, or a combination thereof) of a subject, amounts of CO₂ or another appropriate gas may be measured. By evaluating such measurements, the ELV of the subject may be substantially noninvasively determined, or estimated.

A noninvasive ELV estimation apparatus that incorporates teachings of the present invention is configured (e.g., programmed) to evaluate CO₂ and flow data from a subject and process the same in such a way as to calculate ELV. A system of the present invention includes such an apparatus, as well as CO₂ and flow sensors, which obtain CO₂ and flow measurements in as noninvasive a manner as possible (with the possible exception of an endotracheal tube) and communicate data representative of the measured CO₂ and flow levels to the noninvasive ELV estimation apparatus.

Other features and advantages of the present invention will become apparent to those of ordinary skill in the art through consideration of the ensuing description, the accompanying figures, and the appended claims.

BRIEF DESCRIPTION OF THE FIGURES

In the figures, which illustrate various exemplary aspects of the present invention:

FIG. 1 is a schematic representation of an alveolus of an individual, illustrating the locations at which various respiratory and blood gas parameters may be determined;

FIG. 2 is a graph that illustrates the volume of gases in the carbon dioxide stores of a respiratory tract of an individual (V_(A)) during a series of respiratory cycles, or breaths;

FIG. 3 is a plot of the transformed {circumflex over ({dot over (V)})}_(M)CO₂ data points against c_(ACO2) data points, in which the plotted points are substantially in-line with one another;

FIG. 4 is a schematic representation of an example of a monitoring system incorporating teachings of the present invention; and

FIG. 5 is a line graph showing the correlation between two sets of ELV calculations that have been made in accordance with teachings of the present invention.

DETAILED DESCRIPTION

The present invention includes methods for determining the FRC or ELV of a subject substantially noninvasively. In the inventive methods, FRC or ELV may be determined by evaluating a respiratory gas, such as carbon dioxide, and respiratory flow. Respiratory gas and flow signals may be used to determine a variety of parameters and, along with a mathematical model of the subject's lung, used to determine FRC or ELV. The ensuing description includes a discussion of the manner in which one or more exemplary algorithms are derived, as well as reasoning to support such derivation, to facilitate substantially a noninvasive determination of the subject's FRC or ELV.

In accordance with teachings of the present invention, FRC and ELV may be determined while the respiratory and cardiovascular, or hemodynamic, performance of a subject are being determined in a substantially noninvasive manner. Exemplary measures of the cardiovascular performance of a subject include, but are not limited to, pulmonary capillary blood flow and cardiac output.

The carbon dioxide Fick equation has long been used to determine both pulmonary capillary blood flow and cardiac output. One form of the carbon dioxide Fick equation follows: PCBF=VCO ₂/(c _(vCO2) −c _(ACO2)),  (1) where PCBF represents pulmonary capillary blood flow, VCO₂ is carbon dioxide elimination, c_(vC02) is carbon dioxide content of the venous blood of the monitored individual, and c_(AC02) is the carbon dioxide content of the alveolar (i.e., pulmonary capillary) blood of the monitored individual.

The most accurate way to measure VCO₂ would be to directly measure the flow of CO₂ from the blood within the pulmonary capillaries that surround the alveoli of the lungs to the alveoli, or carbon dioxide excretion ({dot over (V)}_(B)CO₂). If VCO₂ could be measured in this manner, equation (1) becomes: $\begin{matrix} {{PCBF} = \frac{{\overset{.}{V}}_{B}{CO}_{2}}{c_{vCO2} - c_{ACO2}}} & (2) \end{matrix}$ If the content of CO₂ in blood at the alveolus (c_(ACO2)) is substantially the same as the content of CO₂ in arterial blood (c_(aCO2)), then cardiac output ({dot over (Q)}) may be substituted for PCBF in equation (2).

Rearranging equation (2) for a calculation of {dot over (V)}_(B)CO₂ results in the following: {dot over (V)} _(B) CO ₂ =−PCBF c _(ACO2) +PCBF c _(vCO2).  (3)

Notably, equation (3) takes the form of the standard equation for a line in a two-dimensional (x, y) coordinate system: y=m×+b. When {dot over (V)}_(B)CO₂ signals (y-axis) are plotted in a two-dimensional coordinate system against c_(ACO2) signals α-axis) taken at various points during and before or after a change in the effective ventilation of an individual, it can be seen the slope (m) of a line extending through the plotted points will be −PCBF, while PCBF c_(vCO2) is the intercept (b).

Equations (2) and (3) are based on the rate at which carbon dioxide leaves, or is eliminated from, the blood at the alveoli ({dot over (V)}_(B)CO₂). If the flow of CO₂ from the blood into the alveoli, or carbon dioxide excretion ({dot over (V)}_(B)CO₂), could be measured and plotted against c_(ACO2) during rebreathing or another change in the effective ventilation of the subject, data from every breath, including transitional data points, would fall on the line defined by equation (3).

Unfortunately, {dot over (V)} CO₂ is not measured directly at the alveoli. It is measured in a less direct manner—at or near the subject's mouth. Carbon dioxide signals that originate at or near the mouth of a subject are typically obtained and processed, along with respiratory flow signals, to facilitate such measurements. Notably, U.S. Patent Publication U.S. 2002/0183643 A1 of Kück et al. (hereinafter “Kück”), the disclosure of which is hereby incorporated herein, in its entirety, by this reference, teaches that measurements of CO₂ that are taken at the mouth of a subject as the subject exhales do not necessarily correlate well with the amount of CO₂ that is given off by the blood as it passes by the alveoli of the subject's lungs. More specifically, CO₂ that is exhaled, or eliminated, from the subject's respiratory system, as measured at or near the subject's mouth ({dot over (V)}_(M)CO₂) ultimately results from but does not correlate well with the amount of CO₂ that is excreted from the blood to the lungs of the subject ({circumflex over ({dot over (V)})}_(B)CO₂, when considered in terms of flow) during the same breath. Kück explains that such miscorrelation is caused by the CO₂ stores of a subject's lungs, specifically by the buffering capacity of the CO₂ stores.

More specifically, {dot over (V)}_(M)CO₂ includes both {dot over (V)}_(B)CO₂ and CO₂ that has flowed into or out of the ELV of the subject's lungs, which include CO₂ stores ({dot over (V)}_(STORES)CO₂). Thus, {dot over (V)} _(B) CO ₂ ={dot over (V)} _(M) CO ₂ −{dot over (V)} _(STORES) CO ₂.  (4)

The CO₂ stores of a subject's lungs act as a buffer, absorbing some of the increased CO₂ and causing {dot over (V)}_(M)CO₂ to change more gradually than {dot over (V)}_(B)CO₂ changes.

The CO₂ stores of an individual's lungs may be evaluated by use of a model of the lung, such as the simple model of the lung depicted in FIG. 1, in which a single alveolus 100 and a corresponding pulmonary capillary 102 represent the lung. The direction in which blood flows through pulmonary capillary 102 is represented by arrows 103. The mouth of an individual is represented at reference 106. In the model of FIG. 1, the carbon dioxide stores of the lung are depicted, for the purpose of simplicity, as comprising the physical gas volume 104 of the alveolus (V_(A)). As is known in the art, V_(A)is related to tidal volume (V_(T)), as well as to the functional residual capacity (V_(FRC)) of the lung. In addition to the illustrated contributors to the CO₂ stores of the lung (i.e., FRC), CO₂ may be distributed within other stores, such as the alveolar tissues and other tissues of the lung (collectively the ELV). The lung model shown in FIG. 1 also omits V_(T)/V_(Q) mismatch and shunting of blood (i.e., the portion of cardiac output that does not flow through the pulmonary arteries and capillaries, or that is not PCBF). For modeling purposes, the mixing of air within the alveolus (including inspired gases, CO₂ escaping from the blood, flow of CO₂ into and out of the CO₂ stores, and gases within the alveolus) is assumed to occur instantaneously. The effective volume of the CO₂ stores of an individual's lungs are denoted herein as “V_(A) ^(*).”

The effects of the CO₂ stores may be evaluated to obtain an accurate {dot over (V)}_(B)CO₂ based on direct {dot over (V)}_(M)CO₂ measurements. For example, a model of the lung, such as that depicted in FIG. 1, may be evaluated on a breath-by-breath basis. By way of example only, a breath (n) may be delineated as the period from the end of one inspiration to the end of the next inspiration, as illustrated in FIG. 2. In addition, FIG. 2 depicts an example of the effective volume of CO₂ stores in the subject's respiratory tract (e.g., lungs) during the course of respiration.

If the effective volume of CO₂ stores (V_(A) ^(*)) does not change from breath to breath, the amount of CO₂ that flows into and out of the CO₂ stores from one breath to the next may be expressed as a change in alveolar CO₂ fraction (f_(A)CO₂) (i.e., the fraction of gases in the alveolus that comprise CO₂), or the difference between f_(A)CO₂ for a particular breath (f_(A)CO₂(n)) and f_(A)CO₂for the previous breath f_(A)CO₂(n−1). Thus, the volume of the CO₂ stores ({dot over (V)}_(STORES)CO₂) for a particular breath (n) may be determined by multiplying the effective volume in which the CO₂ stores are located (V_(A)*) by the change in f_(A)CO₂from the previous breath (n−1) to the current breath (n) and by the subject's respiratory rate (RR).

Equation (4) then becomes: {dot over (V)} _(B) CO ₂(n)={dot over (V)} _(M) CO ₂(n)+V _(A) ^(*)(n)[f _(A) CO ₂(n)−f _(A) CO ₂(n−1)]RR.  (5) Equation (5) is particularly useful for estimating {dot over (V)}_(B)CO₂from {dot over (V)}_(M)CO₂ measurements that are obtained during the transition from “normal” breathing (e.g., nonrebreathing) to a change in the effective ventilation of the subject (e.g., rebreathing or another change in the effective ventilation). An estimate of {dot over (V)}_(B)CO₂is denoted herein as {circumflex over ({dot over (V)})}_(B)CO₂ and may be substituted for {dot over (V)}_(B)CO₂in equation (5).

While {dot over (V)}_(M)CO₂ and RR may be measured directly, the alveolar CO₂ fraction (f_(ACO2)) and V_(A)* cannot. It is known, however, that f_(ACO2) is proportional to p_(ACO2), which is proportional to p_(etCO2), which may be measured directly (e.g., by use of a capnometer). The p_(etCO2) measurement may then be used, as known in the art, to obtain an f_(ACO2) value for each breath.

V_(A) ^(*) may be adaptively estimated, such as by using the linear correlation between +E,circ {dot over (V)}_(B)CO₂from equation (5), substituting {circumflex over (V)}_(A) ^(*), the estimated effective alveolus volume, for V_(A) ^(*), the actual effective alveolus volume, and using c_(ACO2) as a guide (see equation (3)). The more accurately {circumflex over (V)}_(A) ^(*) reflects V_(A) ^(*), the closer the data points of a plot of +E,circ {dot over (V)}_(B)CO₂against c_(ACO2) (which is also proportional to and may be determined from p_(etCO2)measurements in a manner known in the art) over the course of a change in the effective ventilation of an individual will be to a line representative of the actual pulmonary capillary blood flow or cardiac output of the individual. The ideal value for {circumflex over (V)}_(A) ^(*) may, therefore, be determined as the value that results in the best linear fit between the plotted data (C_(ACO2) against +E,circ {dot over (V)}_(B)CO₂) and, thus, a maximized correlation coefficient, or r² value. By way of example only, an adaptive, iterative, or search algorithm of a type known in the art may be used to determine {circumflex over (V)}_(A) ^(*) for which the correlation coefficient, or r², is maximized. The graph of FIG. 3 shows an example of a {circumflex over (V)}_(A) ^(*) value at which r² is maximized.

Once an accurate {circumflex over (V)}_(A) ^(*) estimate has been made, the effective volume of the FRC (V_(FRC)) or ELV (V_(ELV)) of the subject's lungs may also be estimated or determined. In this regard, equation (5) may be rewritten, as follows, to reflect the use of {circumflex over (V)}_(A) ^(*) as an estimate for V_(A) ^(*): {circumflex over ({dot over (V)})} _(B) CO ₂(n)={dot over (V)} _(M) CO ₂(n)+{circumflex over (V)}_(A) ^(*)(n)[f _(ACO2)(n)−f _(ACO2)(n−1)]RR.  (6)

The foregoing approach (particularly, the use of equation (6)) works well when a subject is mechanically ventilated (i.e., on a respirator), in which case the respiratory rate and tidal volume (V_(T)) of the individual's respiration are typically substantially stable, which provides for a “clean” f_(ACO2) signal.

During spontaneous or mixed (i.e., mechanical and spontaneous) ventilation, it may be desirable to eliminate any noise that may occur in the f_(ACO2) signal when equation (6) is used, as such noise may result in an inaccurate estimation of {dot over (V)}_(B)CO₂(i.e., {circumflex over ({dot over (V)})}_(B)CO₂). An algorithm that is less sensitive to noise than equation (6) may, therefore, also be useful for estimating {circumflex over ({dot over (V)})}_(B)CO₂, as described hereinafter.

Assuming that pulmonary capillary blood flow and cardiac output do not change from one breath to the next, the carbon dioxide Fick equation (equation (2)) may be rewritten for two successive breaths: $\begin{matrix} {{PCBF} = {\frac{{\overset{.}{V}}_{B}{{CO}_{2}\left( {n - 1} \right)}}{{c_{vCO2}\left( {n - 1} \right)} - {c_{ACO2}\left( {n - 1} \right)}} = \frac{{\overset{.}{V}}_{B}{{CO}_{2}(n)}}{{c_{vCO2}(n)} - {c_{ACO2}(n)}}}} & (7) \end{matrix}$ Further, assuming that c_(vCO2) does not change from one breath to the next, equation (7) may be simplified to: $\begin{matrix} {{PCBF} = \frac{{{\overset{.}{V}}_{B}{{CO}_{2}\left( {n - 1} \right)}} - {{\overset{.}{V}}_{B}{{CO}_{2}(n)}}}{{c_{ACO2}(n)} - {c_{ACO2}\left( {n - 1} \right)}}} & (8) \end{matrix}$

Measurements of the CO₂ fraction of gases in a subject's alveoli (f_(ACO2)) may be used in place of the c_(ACO2) measurements of equation (8) when the slope of the CO₂ dissociation curve (s_(CO2)), a standard curve which illustrates the rate at which CO₂ molecules dissociate from the hemoglobin molecules of red blood cells, and barometric pressure (p_(baro)) are also taken into consideration, as known in the art. Accordingly, equation (8) may be rewritten as follows: $\begin{matrix} {{PCBF} = \frac{{{\overset{.}{V}}_{B}{{CO}_{2}\left( {n - 1} \right)}} - {{\overset{.}{V}}_{B}{{CO}_{2}(n)}}}{{s_{CO2}\quad p_{baro}\quad{f_{ACO2}(n)}} - {f_{ACO2}\left( {n - 1} \right)}}} & (9) \end{matrix}$ Solving this expression for the difference in CO₂ fractions (f_(ACO2)(n)−f_(ACO2)(n−1)) yields: $\begin{matrix} {{{f_{ACO2}(n)} - {f_{ACO2}\left( {n - 1} \right)}} = \frac{{{\overset{.}{V}}_{B}{{CO}_{2}\left( {n - 1} \right)}} - {{\overset{.}{V}}_{B}{{CO}_{2}(n)}}}{s_{CO2}\quad p_{baro}\quad{PCBF}}} & (10) \end{matrix}$ Substitution of equation (10) into equation (6) results in: $\begin{matrix} \begin{matrix} {{{\overset{\hat{.}}{V}}_{B}{{CO}_{2}(n)}} = {{{\overset{.}{V}}_{M}{{CO}_{2}(n)}} +}} \\ {\frac{{RR}\quad{\hat{V}}_{A}*(n)}{s_{CO2}\quad p_{baro}\quad{PCBF}}\left\lbrack {{{\overset{\hat{.}}{V}}_{B}{{CO}_{2}\left( {n - 1} \right)}} - {{\overset{\hat{.}}{V}}_{B}{{CO}_{2}(n)}}} \right\rbrack} \end{matrix} & (11) \end{matrix}$ This expression can now be solved for {circumflex over ({dot over (V)})}_(B)CO₂(n) to provide an accurate estimate of {dot over (V)}_(B)CO₂: $\begin{matrix} \begin{matrix} {{{\overset{\hat{.}}{V}}_{B}{{CO}_{2}(n)}} = {{\frac{1}{\frac{1 + {{RR}\quad{\hat{V}}_{A}*(n)}}{s_{CO2}\quad p_{baro}\quad{PCBF}}}\quad{\overset{.}{V}}_{M}{{CO}_{2}(n)}} +}} \\ {\frac{\frac{{RR}\quad{\hat{V}}_{A}*(n)}{s_{CO2}\quad p_{baro}\quad{PCBF}}}{1 + \frac{{RR}\quad V_{A}*(n)}{s_{CO2}\quad p_{baro}\quad{PCBF}}}\quad{\overset{\hat{.}}{V}}_{B}{{CO}_{2}\left( {n - 1} \right)}} \end{matrix} & (12) \end{matrix}$ Structurally, this result represents a first order, single-pole low pass filter of the form {circumflex over ({dot over (V)})} _(B) CO ₂(n)=(1−α){dot over (V)} _(M) CO ₂(n)+α{circumflex over ({dot over (V)})} _(B) CO ₂(n−1),  (13) where α, the transformation coefficient, may be represented as $\begin{matrix} {\frac{\frac{{RR}\quad{\hat{V}}_{A}*(n)}{s_{CO2}\quad p_{baro}\quad{PCBF}}}{1 + \frac{{RR}\quad V_{A}*(n)}{s_{CO2}\quad p_{baro}\quad{PCBF}}}.} & (14) \end{matrix}$

The RR in equation (14), which is the respiratory rate of the subject, is measured in breaths per minute. {circumflex over (V)}_(A) ^(*) (n) is estimate of the CO₂ stores of the subject's lungs during breath (n) and is approximately equivalent to the volume of the FRC or ELV of the subject's lungs (V_(FRC)* and V_(ELV)*, respectively). SCO₂ is the slope of the standard carbon dioxide dissociation curve. p_(baro) is barometric pressure. PCBF, the pulmonary capillary blood flow the subject, does not need to be known to determine either α or {circumflex over (V)}_(A) ^(*) (n).

It is not necessary to know PCBF to calculate a because a determination of a merely requires that the linearity, or straightness, of a line through {dot over (V)}_(B)CO₂ values that have been plotted against p_(etCO2) or c_(CO2) values be evaluated, not that the slope of the line, which is equal to PCBF, be evaluated. In that regard, the transformation coefficient (α) in equations (13) and (14) may be determined iteratively, by using an initial a value, then progressively increasing and/or decreasing the α value to determine the α value that provides for a plot of {dot over (V)}_(B)CO₂ values against p_(etCO2) or c_(CO2) values with the greatest linearity (as opposed to an open loop) or, stated another way, that provides an optimal correlation coefficient (r2) between the {dot over (V)}_(B)CO₂ values and the p_(etCO2) or c_(CO2) values. Other methods for determining an optimal α value include, without limitation, rote searching, global searching, gradient searching (e.g., use of a gradient descent search algorithm), use of a least mean squares algorithm, use of other predetermined equations or sets of predetermined equations, use of a truly adaptive filtering technique, and use of other techniques to determine the optimal a value, as known in the art.

Use of an optimal transformation coefficient (α) (equation (14)) in equation (13) provides a relatively accurate, simple mathematical model of the lung of a subject. The algorithm of equation (13) may be used to calculate the amount of CO₂ that flows into and out of the carbon dioxide stores of the lungs on a “breath-to-breath” basis.

The {circumflex over (V)}_(A)* (n) of equation (14) is equivalent to ELV and flow may be converted to volume, which results in elimination of RR, allowing a to be expressed more simply as: $\begin{matrix} {{\alpha = \frac{{\hat{V}}_{A}*}{{s_{CO2}\quad p_{baro}\quad{{PCBF}/{RR}}} + {{\hat{V}}_{A}*}}},} & (15) \end{matrix}$ where Q is measured in terms of volume, rather than flow. If equation (15) were multiplied through with Δf_(ACO2) (i.e., f_(ACO2)(n)−f_(ACO2)(n−1), the expression could be viewed as calculating the relative amount of CO₂ stored in ELV over the total change in the amount of CO₂ from a change in the effective ventilation of a subject (e.g., rebreathing or another change in effective ventilation).

If PCBF/RR is calculated from data obtained before and during a change in the effective ventilation of the subject (e.g., rebreathing or another change in effective ventilation), equation (15) may be rewritten as follows: $\begin{matrix} {\alpha = \frac{{\hat{V}}_{A}*}{\frac{\Delta\quad V\quad{CO}_{2}}{\Delta\quad f_{CO2}} + {{\hat{V}}_{A}*}}} & (16) \end{matrix}$ Equation (16) may be rearranged as follows: $\begin{matrix} {{\hat{V}}_{A}^{*} = {\frac{\alpha}{1 - \alpha}\left( {{PCBF}/{RR}} \right)s_{CO2}p_{Baro}}} & (17) \end{matrix}$ to solve for ELV ({circumflex over (V)}_(A)*)

Equation (17) may be used to substantially noninvasively determine ELV when virtually any change in the effective ventilation of the subject (e.g., rebreathing, change in respiratory rate, change in respiratory volume, etc.) has occurred, whether or not the subject continues to breathe as data is collected, with data obtained during “normal” breathing being compared with data obtained once the change in effective ventilation has occurred.

Other techniques for determining an optimal α value are also within the scope of the present invention.

Equation (6) does not take into account the possibility, or even likelihood, that the amount of CO₂ stored within the lungs ({dot over (V)}_(STORES)CO₂) may vary from breath to breath. A more complex version of equation (6) accounts for this possibility: {circumflex over ({dot over (V)})} _(B) CO ₂(n)={dot over (V)} _(M) CO ₂(n)+({circumflex over (V)} _(A) ^(*)(n)+V _(T)(n))×(f _(ACO2)(n)−f _(ACO2)(n−1))+(V _(T)(n)−V _(T)(n−1))×f _(ACO2)(n),  (18)

Accordingly, in another aspect, the present invention includes use of an algorithm that corrects ELV for possible changes in V_(CO2STORES) and combines the ELV correction with the CO₂ form of the differential Fick equation: $\begin{matrix} {{\overset{.}{Q} = {\frac{{{\overset{\_}{V}}_{M}{CO}_{2}} - \left( {{{\overset{.}{V}}_{M}{{CO}_{2}(n)}} + {{\hat{V}}_{A}^{*} \cdot \left\lbrack {{f_{ACO2}(n)} - {f_{ACO2}\left( {n - 1} \right)}} \right\rbrack}} \right.}{s_{CO2} \cdot \left( {{p_{ACO2}(n)} - {\overset{\_}{p}}_{ACO2}} \right)} \times {RR}}},} & (19) \end{matrix}$ where {overscore (V)}_(M)CO₂ is the average breath-to-breath volume, not flow, of carbon dioxide eliminated from the subject's lungs, as measured at the mouth, during breaths that precede and effective change in the ventilation of the subject (e.g., rebreathing or another change in effective ventilation). The ELV value of equation (19) includes tidal volume (V_(T)). For a closer estimate of FRC, the inspiratory tidal volume should be subtracted from ELV, as estimated for use in equation (19). Notably, accurate results may be obtained when {dot over (V)}_(M)CO₂ (n) for each breath is calculated from expiration to inspiration (i.e., as {dot over (V)}_(M)CO₂ (n)={dot over (V)}_(M)CO_(2expired)(n−1)−{dot over (V)}_(M)CO_(2inspired)(n)).

Tidal volumes typically do not change drastically from breath-to-breath. Therefore, the expression V_(T)(n)−V_(T)(n−1) from equation (18) has been omitted from equation (19) without substantially affecting the accuracy of a subsequent ELV determination. Optionally however, a variation of equation (19) may consider the change in tidal volume from one breath to the next, as doing so could improve the accuracy of the {dot over (Q)} calculation and, thus, of the subsequent ELV estimation.

If {dot over (V)}_(M)CO₂ and p_(etCO2) reach good plateaus within a cycle, it might be possible to use them to calculate PCBF in equation (19). This is possible because ELV does not affect PCBF estimations from plateau values (algebraically, the f_(ACO2)(n)−f_(ACO2) (n−1) term vanishes at plateaus).

Equation (19) can be solved for ELV ({circumflex over (V)}_(A)*): $\begin{matrix} {{\hat{V}}_{A}^{*} = {\frac{1}{{f_{ACO2}(n)} - {f_{ACO2}\left( {n - 1} \right)}} \cdot \left\lbrack {{V_{M}{CO}_{2{PRE}}} - {V_{M}{{CO}_{2}(n)}} - {{PCBF} \cdot s_{CO2} \cdot \left( {{p_{ACO2}(n)} - p_{{ACO2}\quad{PRE}}} \right) \cdot \frac{1}{RR}}} \right\rbrack}} & (20) \end{matrix}$

Furthermore, if it is assumed that one CO₂ dissociation curve slope s_(CO2) (e.g., the average across the cycle's p_(etCO2) values) can be used, then it cancels and the equation simplifies to: $\begin{matrix} {{\hat{V}}_{A}^{*} = {\frac{1}{{f_{ACO2}(n)} - {f_{ACO2}\left( {n - 1} \right)}} \cdot \left\lbrack {{V_{M}{CO}_{2{PRE}}} - {V_{M}{{CO}_{2}(n)}} - {\frac{{V_{M}{CO}_{2{PRE}}} - {V_{M}{CO}_{2{DUR}}}}{p_{{ACO2}\quad{DUR}} - p_{{ACO2}\quad{PRE}}} \cdot \left( {{p_{ACO2}(n)} - p_{{ACO2}\quad{PRE}}} \right)}} \right\rbrack}} & (21) \end{matrix}$ where the pre and during values represent the respective plateaus. Alternatively, PCBF can be determined through some other method, be it invasive (e.g., thermodilution), or noninvasive (e.g., electrical bioimpedance).

Parts of equation (21) may be used in at least two embodiments of the present invention, one of which includes use of the first part of equation (21) to determine ELV. More specifically, if one could assume that {dot over (V)}_(B)CO₂ is constant even though the p_(ACO2) is changing due to a change in the effective ventilation of the subject (e.g., rebreathing or another change in effective ventilation), ELV may be determined as follows: $\begin{matrix} {{\hat{V}}_{A}^{*} = {\frac{1}{{f_{ACO2}(n)} - {f_{ACO2}\left( {n - 1} \right)}} \cdot \left\lbrack {{V_{M}{CO}_{2{PRE}}} - {V_{M}{{CO}_{2}(n)}}} \right\rbrack}} & (22) \end{matrix}$

Equation (22) may be used to evaluate ELV when a change in the effective ventilation of the subject (e.g., rebreathing, change in respiratory rate, change in respiratory volume, etc.) has been effected, and while the subject continues to breathe (i.e., not during maneuvers which require breath-holding or which otherwise temporarily terminate breathing). In using equation (22) to determine ELV, data obtained during “normal” breathing may be compared with data obtained once the change in effective ventilation has occurred. For example, and not by way of limitation, breath (n−1) may represent a normal breath, while (n) may represent the first breath in which the change in effective ventilation has occurred.

The second of these embodiments employs both the first part of equation (21) (i.e., equation (22), as well as the second part of equation (21): $\begin{matrix} \left. {{- \frac{{V{CO}}_{2{PRE}} - {V{CO}}_{2{DUR}}}{p_{{ACO2}\quad{DUR}} - p_{{ACO2}\quad{PRE}}}} \cdot \left( {{p_{ACO2}(n)} - p_{{ACO2}\quad{PRE}}} \right)} \right\rbrack & (23) \end{matrix}$ or a broader variation thereof: $\begin{matrix} {{PCBF} \cdot s_{CO2} \cdot \frac{1}{RR} \cdot \left( {{p_{ACO2}(n)} - p_{{ACO2}\quad{PRE}}} \right)} & (24) \end{matrix}$ In this manner, the ELV calculation of equation (22) may be modified to compensate for changes in p_(AC02) during a breath, or continuously changing p_(ACO2). Specifically, the ratio of the change in VCO₂ to the change in p_(AC02) in equation (23) and of {dot over (Q)} in equation (24) represents the slope of the line that describes the amount of CO₂ that exits the CO₂ stores through the mouth as CO₂ exiting the blood is added to the CO₂ stores, or the “sensitivity” with which changes in p_(etCO2) represent changes in p_(AC02) as CO₂ from the blood flows into the CO₂ stores, which in turn provides an indication of buffering capacity of the CO₂ stores. (p_(ACO2)(n)−{overscore (p)}_(AC02)) provides an indication of the magnitude of the p_(ACO2) change to be scaled when p_(etCO2) is measured at or near the mouth.

The $\frac{1}{RR}$ in equation (24) may be substituted with a different value that represents the time interval between the start of a change in effective ventilation (e.g., rebreathing) and the time when the measured p_(AC02) left the alveoli. Generally, such a value will be less than $\frac{1}{RR}.$

The combination of equations (23) and (24) may be used to substantially noninvasively determine ELV when virtually any change in the effective ventilation of the subject has occurred, whether or not the subject continues to breathe as data is collected. More specifically, data obtained during “normal” breathing may be compared with data obtained once the change in effective ventilation has occurred.

Turning now to FIG. 4, an exemplary diagnostic system 1 that incorporates teachings of the present invention is schematically illustrated. Diagnostic system 1 includes, among other things, an airway 52 in communication with the airway A of an individual I, as well as a flow meter 72 and a carbon dioxide sensor 74 positioned along airway 52. Flow meter 72 and carbon dioxide sensor 74 communicate signals to corresponding monitors 73 and 75, which communicate electronically with a processor 82 of a respiratory monitor 80 (e.g., the processor and respiratory monitor of a NICO® monitor available from Novametrix Medical Systems (Wallingford, Conn.) division of Respironics, Inc). Processor 82 is programmed to determine at least VCO₂ and p_(etCO2) based on signals communicated thereto from flow meter 72 and carbon dioxide sensor 74. In addition, processor 82 may be programmed to use signals from one or both of flow meter 72 and carbon dioxide sensor 74 or calculated parameters (e.g., VCO₂ and p_(etCO2)) in the above-described algorithms (i.e., one or more of equations (1)-(24)) to facilitate the substantially noninvasive and accurate determination of individual I's ELV. Alternatively, such calculations may be made manually.

In a method that incorporates teachings of the present invention, VCO₂ and p_(etCO2) values are obtained during both a baseline, or first, ventilatory state, and when a change in the effective ventilation of individual I has been effected, or a second ventilatory state. Alternatively, such values may obtained during a transition between first and second states, then compared with values obtained during the first or second state.

The first ventilatory state may be effected under substantially “normal” breathing conditions. Alternatively, the baseline ventilatory state may be defined under a first set of other, selected breathing conditions. The second ventilatory state occurs when one or more respiratory control parameters are manipulated to achieve breathing conditions differ from those present during the first ventilatory state to a degree that effect a measurable change in minute ventilation.

The second ventilatory state may be induced, for example, by altering the value of a limit variable, e.g., inspiratory pressure, tidal volume, flow rate or time, from a value of the limit variable during the first ventilatory state. In another exemplary method, a change in effective ventilation may be induced by altering the threshold value of a cycle variable from the threshold level of the cycle variable during the first ventilatory state. In a further exemplary method, a change in effective ventilation may be induced by altering the threshold triggering value of a triggering variable, such as inspiratory pressure or flow rate. In a still further method, a change in effective ventilation may be induced by delivering to the individual a series of at least three “sigh breaths,” which are deeper than normal breaths. Changes in effective ventilation may also comprise periods of unsteady, or “noisy,” breathing.

The VCO₂ and p_(etCO2) values that are obtained are then processed in accordance with one or more of equations (1)-(24)) to substantially noninvasively and accurately determine individual I's ELV.

EXAMPLE

Different effective FRC values were achieved by incrementally advancing an especially long endotracheal tube from an initial, normal position to a small distance within the bronchial tree of an anesthetized pig (at time=15:26) and, twenty-one minutes later (at time=15:47) to a position further within the bronchial tree. By ventilating only parts of the lung, the effective FRC was reduced with each advancement of the endotracheal tube.

ELV was calculated for various breaths using equation (18). ELV values that were calculated when a sufficient f_(ACO2)(n)−f_(ACO2)(n−1) threshold was present and during certain breaths (e.g., the second breath into rebreathing, the first breath of recovery, etc.) were considered valid and are included as data points in the graph of FIG. 5. Notably, the plotted data points represent ELV minus inspiratory tidal volume. ELV values that were calculated from data obtained during transition from normal breathing into rebreathing are shown as diamond-shaped points. ELV values that were calculated from data obtained during the transition from rebreathing to recovery are shown as squares. The closeness of the lines that extend through the two sets of data indicates that the ELV values and, thus, the algorithm (equations (22 and 23)) from which they were calculated provides reasonable ELV values. Notably, the trends of the two sets of ELV calculations decrease, as expected, at times when the endotracheal tube was advanced further into the lungs of the pig. These trends, as well as their magnitude, are confirmed by the underlying VCO₂ signals 50 and p_(etCO2) signals 51. Moreover, the ELV estimations remained relatively stable even when severe changes in p_(etCO2) were noted (see the p_(etCO2) trend after 15:50).

Although the foregoing description contains many specifics, these should not be construed as limiting the scope of the present invention, but merely as providing illustrations of some of the presently preferred embodiments. Similarly, other embodiments of the invention may be devised which do not depart from the spirit or scope of the present invention. Features from different embodiments may be employed in combination. The scope of the invention is, therefore, indicated and limited only by the appended claims and their legal equivalents, rather than by the foregoing description. All additions, deletions and modifications to the invention as disclosed herein which fall within the meaning and scope of the claims are to be embraced thereby. 

1. A method for substantially noninvasively estimating effective lung volume of a subject, comprising: effecting a change in effective ventilation of a subject; and determining an effective lung volume that results in a substantially linear relationship between carbon dioxide elimination measured at or near the mouth of the subject and a concentration of carbon dioxide in gas exhaled from the alveoli of the subject's lungs when applied to the carbon dioxide elimination measured at the mouth to compensate for flow of carbon dioxide into the effective lung volume.
 2. The method of claim 1, wherein determining comprises: selecting a linear filter coefficient that creates a substantially linear relationship between the carbon dioxide elimination and the concentration of carbon dioxide.
 3. The method of claim 1, wherein determining the effective lung volume comprises selecting the effective lung volume providing an optimal correlation between the carbon dioxide elimination and the carbon dioxide concentration.
 4. The method of claim 1, wherein determining the effective lung volume comprises employing the following algorithm: ${{\hat{V}}_{A}^{*} = \frac{\alpha}{1 - \alpha}},$ where {circumflex over (V)}_(A)* represents the effective lung volume and a represents the optimal correlation between the carbon dioxide elimination and the carbon dioxide concentration.
 5. The method of claim 1, wherein effecting includes rebreathing.
 6. A method for substantially noninvasively estimating effective lung volume of a subject, comprising: effecting a change in effective ventilation of a subject while the subject continues to breathe; considering a change in the concentration of carbon dioxide in gases residing within the alveoli of the subject's lungs from baseline breathing to breathing in which the change in effective ventilation is effected; and considering a change in carbon dioxide elimination from baseline breathing to breathing in which the change in effective ventilation is effected.
 7. The method of claim 6, wherein considering the change in concentration and considering the change in carbon dioxide elimination comprise employing the following algorithm: ${{\hat{V}}_{A}^{*} = {\frac{1}{{f_{ACO2}(n)} - {f_{ACO2}\left( {n - 1} \right)}} \cdot \left\lbrack {{V_{M}{CO}_{2{PRE}}} - {V_{M}{{CO}_{2}(n)}}} \right\rbrack}},$ where {circumflex over (V)}_(A)* represents the effective lung volume, f_(ACO2)(n) and f_(ACO2)(n−1) represent the concentration of carbon dioxide during successive breaths, only one of which occurs when a change effective ventilation has been effected, V_(M)CO_(2 PRE) represents the carbon dioxide elimination measured at or near the mouth of the subject during baseline breathing, and V_(M)CO₂(n) represents the carbon dioxide elimination measured for breath (n).
 8. The method of claim 6, wherein effecting includes rebreathing.
 9. A method for substantially noninvasively estimating effective lung volume of a subject, comprising: effecting a change in effective ventilation of a subject; considering a change in the amount of carbon dioxide in gases residing within the alveoli of the subject's lungs from baseline breathing to breathing in which the change in effective ventilation is effected; considering a change in carbon dioxide elimination from baseline breathing to breathing in which the change in effective ventilation is effected; and compensating for changes in the amount of carbon dioxide in gases residing within the alveoli that occur during a breath.
 10. The method of claim 9, wherein compensating comprises: considering the change in carbon dioxide delivered to a lung from blood as a result of the change in effective ventilation that was effected.
 11. The method of claim 10, wherein compensating further comprises: considering a magnitude of the change in the amount of carbon dioxide in the alveoli from baseline breathing to breathing in which the change in effective ventilation is effected.
 12. The method of claim 9, wherein effecting includes rebreathing.
 13. The method of claim 9, wherein effecting includes breath-holding.
 14. The method of claim 9, wherein considering the change in the concentration of carbon dioxide, considering the change in carbon dioxide elimination, and compensating for changes in the amount of carbon dioxide comprise employing the following algorithm: ${{\hat{V}}_{A}^{*} = {\frac{1}{{f_{ACO2}(n)} - {f_{ACO2}\left( {n - 1} \right)}} \cdot \left\lbrack {{V_{M}{CO}_{2{PRE}}} - {V_{M}{{CO}_{2}(n)}} - {\frac{{V_{M}{CO}_{2{PRE}}} - {V_{M}{CO}_{2{DUR}}}}{p_{ACO2DUR} - p_{ACO2PRE}} \cdot \left( {{p_{ACO2}(n)} - p_{ACO2PRE}} \right)}} \right\rbrack}}\quad$ where {circumflex over (V)}_(A)* represents the effective lung volume, f_(ACO2)(n) and f_(ACO2)(n−1) represent the concentration of carbon dioxide during successive breaths, only one of which occurs when a change effective ventilation has been effected, V_(M)CO_(2 PRE) represents the carbon dioxide elimination measured at or near the mouth of the subject during baseline breathing, V_(M)CO₂ (n) represents the carbon dioxide elimination measured for breath (n), V_(M)CO_(2 DUR) represents the carbon dioxide elimination measured at or near the mouth when the change in effective ventilation has been effected, p_(ACO2) PRE represents the partial pressure of carbon dioxide within the alveoli of the subject's lung during baseline breathing, and p_(ACO2)(n) represents the partial pressure of carbon dioxide within the alveoli during breath (n).
 15. The method of claim 9, wherein considering the change in the concentration of carbon dioxide, considering the change in carbon dioxide elimination, and compensating for changes in the amount of carbon dioxide comprise employing the following algorithm: ${{{\hat{V}}_{A}^{*} = {\frac{1}{{f_{ACO2}(n)} - {f_{ACO2}\left( {n - 1} \right)}} \cdot \left\lbrack {{V_{M}{CO}_{2{PRE}}} - {V_{M}{{CO}_{2}(n)}} - {{PCBF} \cdot S_{CO2} \cdot \frac{1}{RR} \cdot \left( {{p_{ACO2}(n)} - p_{ACO2PRE}} \right)}} \right\rbrack}},}\quad$ where V_(A)* represents the effective lung volume, f_(ACO2)(n) and f_(ACO2)(n−1) represent the concentration of carbon dioxide during successive breaths, only one of which occurs when a change effective ventilation has been effected, V_(M)CO_(2 PRE) represents the carbon dioxide elimination measured at or near the mouth of the subject during baseline breathing, V_(M)CO₂ (n) represents the carbon dioxide elimination measured for breath (n), PCBF represents the pulmonary capillary blood flow of the subject, s_(CO2) represents the slope of a standard carbon dioxide dissociation curve, RR represents the subject's respiratory rate, p_(ACO2 PRE) represents the partial pressure of carbon dioxide within the alveoli of the subject's lung during baseline breathing, and p_(ACO2)(n) represents the partial pressure of carbon dioxide within the alveoli during breath (n).
 16. Apparatus for substantially noninvasively estimating effective lung volume of a subject, comprising: means for effecting a change in effective ventilation of a subject; and means for determining an effective lung volume that results in a substantially linear relationship between carbon dioxide elimination measured at or near the mouth of the subject and a concentration of carbon dioxide in gas exhaled from the alveoli of the subject's lungs when applied to the carbon dioxide elimination measured at the mouth to compensate for flow of carbon dioxide into the effective lung volume.
 17. The apparatus of claim 16, wherein the means for determining comprises: means for selecting a linear filter coefficient that creates a substantially linear relationship between the carbon dioxide elimination and the concentration of carbon dioxide.
 18. The apparatus of claim 16, wherein the means for determining the effective lung volume comprises means for selecting the effective lung volume providing an optimal correlation between the carbon dioxide elimination and the carbon dioxide concentration.
 19. The apparatus of claim 16, wherein the means for determining the effective lung volume comprises means for employing the following algorithm: ${{\hat{V}}_{A}^{*} = \frac{\alpha}{1 - \alpha}},$ where {circumflex over (V)}_(A)* represents the effective lung volume and a represents the optimal correlation between the carbon dioxide elimination and the carbon dioxide concentration.
 20. The method of claim 16, wherein the means for effecting includes means for effecting rebreathing.
 21. Apparatus for substantially noninvasively estimating effective lung volume of a subject, comprising: means for effecting a change in effective ventilation of a subject while the subject continues to breathe; means for considering a change in the concentration of carbon dioxide in gases residing within the alveoli of the subject's lungs from baseline breathing to breathing in which the change in effective ventilation is effected; and means for considering a change in carbon dioxide elimination from baseline breathing to breathing in which the change in effective ventilation is effected.
 22. The apparatus of claim 21, wherein the means for considering the change in concentration and considering the change in carbon dioxide elimination comprise means for employing the following algorithm: ${{\hat{V}}_{A}^{*} = {\frac{1}{{f_{ACO2}(n)} - {f_{ACO2}\left( {n - 1} \right)}} \cdot \left\lbrack {{V_{M}{CO}_{2{PRE}}} - {V_{M}{{CO}_{2}(n)}}} \right\rbrack}},$ where {circumflex over (V)}_(A)* represents the effective lung volume, f_(ACO2)(n) and f_(ACO2)(n−1) represent the concentration of carbon dioxide during successive breaths, only one of which occurs when a change effective ventilation has been effected, V_(M)CO_(2 PRE) represents the carbon dioxide elimination measured at or near the mouth of the subject during baseline breathing, and V_(M)CO₂(n) represents the carbon dioxide elimination measured for breath (n).
 23. The apparatus of claim 21, wherein the means for effecting includes means for effecting rebreathing.
 24. Apparatus for substantially noninvasively estimating effective lung volume of a subject, comprising: means for effecting a change in effective ventilation of a subject; means for considering a change in the amount of carbon dioxide in gases residing within the alveoli of the subject's lungs from baseline breathing to breathing in which the change in effective ventilation is effected; and means for considering a change in carbon dioxide elimination from baseline breathing to breathing in which the change in effective ventilation is effected; and means for compensating for changes in the amount of carbon dioxide in gases residing within the alveoli that occur during a breath.
 25. The apparatus of claim 24, wherein the means for compensating comprises: means for considering the change in carbon dioxide delivered to a lung from blood as a result of the change in effective ventilation that was effected.
 26. The apparatus of claim 25, wherein the means for compensating comprise: means for considering a magnitude of the change in the amount of carbon dioxide in the alveoli from baseline breathing to breathing in which the change in effective ventilation is effected.
 27. The apparatus of claim 24, wherein means for effecting includes means for rebreathing.
 28. The apparatus of claim 24, wherein means for effecting includes means for effecting breath-holding.
 29. The apparatus of claim 24, wherein means for considering the change in the concentration of carbon dioxide, the means for considering the change in carbon dioxide elimination, and the means for compensating for changes in the amount of carbon dioxide comprise means for employing the following algorithm: ${{\hat{V}}_{A}^{*} = {\frac{1}{{f_{ACO2}(n)} - {f_{ACO2}\left( {n - 1} \right)}} \cdot \left\lbrack {{V_{M}{CO}_{2{PRE}}} - {V_{M}{{CO}_{2}(n)}} - {\frac{{V_{M}{CO}_{2{PRE}}} - {V_{M}{CO}_{2{DUR}}}}{p_{ACO2DUR} - p_{ACO2PRE}} \cdot \left( {{p_{ACO2}(n)} - p_{ACO2PRE}} \right)}} \right\rbrack}}\quad$ where {circumflex over (V)}_(A)* represents the effective lung volume, f_(ACO2)(n) and f_(ACO2)(n−1) represent the concentration of carbon dioxide during successive breaths, only one of which occurs when a change effective ventilation has been effected, V_(M)CO_(2 PRE) represents the carbon dioxide elimination measured at or near the mouth of the subject during baseline breathing, V_(M)CO₂ (n) represents the carbon dioxide elimination measured for breath (n), V_(M)CO_(2 DUR) represents the carbon dioxide elimination measured at or near the mouth when the change in effective ventilation has been effected, p_(ACO2 PRE) represents the partial pressure of carbon dioxide within the alveoli of the subject's lung during baseline breathing, and p_(ACO2)(n) represents the partial pressure of carbon dioxide within the alveoli during breath (n).
 30. The apparatus of claim 24, wherein the means for considering the change in the concentration of carbon dioxide, the means for considering the change in carbon dioxide elimination, and the means for compensating for changes in the amount of carbon dioxide comprise means for employing the following algorithm: ${{{\hat{V}}_{A}^{*} = {\frac{1}{{f_{ACO2}(n)} - {f_{ACO2}\left( {n - 1} \right)}} \cdot \left\lbrack {{V_{M}{CO}_{2{PRE}}} - {V_{M}{{CO}_{2}(n)}} - {{PCBF} \cdot S_{CO2} \cdot \frac{1}{RR} \cdot \left( {{p_{ACO2}(n)} - p_{ACO2PRE}} \right)}} \right\rbrack}},}\quad$ where {circumflex over (V)}_(A)* represents the effective lung volume, f_(ACO2)(n) and f_(ACO2)(n−1) represent the concentration of carbon dioxide during successive breaths, only one of which occurs when a change effective ventilation has been effected, V_(M)CO_(2 PRE) represents the carbon dioxide elimination measured at or near the mouth of the subject during baseline breathing, V_(M)CO₂ (n) represents the carbon dioxide elimination measured for breath (n), PCBF represents the pulmonary capillary blood flow of the subject, s_(CO2) represents the slope of a standard carbon dioxide dissociation curve, RR represents the subject's respiratory rate, p_(ACO2 PRE) represents the partial pressure of carbon dioxide within the alveoli of the subject's lung during baseline breathing, and p_(ACO2)(n) represents the partial pressure of carbon dioxide within the alveoli during breath (n). 